Don't take the FBI polygraph. You have nothing to gain, and much to lose. The polygraph is nothing more than an interrogational prop in this context, and your "failing" may even be a pre-scripted part of the interrogation plan. The FBI has a deliberate policy of NOT recording polygraph interrogations, freeing their polygraphers to use abusive and manipulative techniques, confident in the knowledge that the suspect (you) will have no way of proving in a court of law what was actually said in the polygraph suite.
You might check whether you are eligible for legal representation by the JAG corps, or if not, whether they can refer you to a local legal aid society.